Industrial Air Quality and Ventilation

204 Industrial Air Quality and Ventilation

© 2010 Taylor & Francis Group, LLC

or

u

u

rr

u

E

m

e

=−

−

()

≤

()

2

0

,.

υ (4.445)

As we can see, in case of a downward initial ow in the duct, it would only be pos-

sible at restriction degrees

r < 2. (4.446)

The length of the zone x

e

− x

m

(which we will name the initial eddy run length) is

determined using Equation 4.438

lx

x

rr

r

u

r

uu

Hem

me

≡− =

−

()

−

()

+

−

()













⋅

−

22

1

2

1

22

mm

em

e

m

uu

rr

r

u

u11

22

1

1

1

2

−

()

−

()

+

−

()

−

()

−

−

ln

.

(4.447)

The equality condition (4.438) determines changes in velocity on this run. Further

velocity increases u become impossible because the function R(r,u) turns negative;

therefore,

du

dx

<

0,

that is, air begins to escape ...